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Journal Article

The Gradient Flow of the Möbius Energy Near Local Minimizers

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Blatt,  Simon
Geometric Analysis and Gravitation, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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CV_Blatt.pdf
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CV43_403.pdf
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Citation

Blatt, S. (2012). The Gradient Flow of the Möbius Energy Near Local Minimizers. Calculus of variations and partial differential equations, 43, 403-439. doi:10.1007/s00526-011-0416-9.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-69B5-D
Abstract
In this article we show that for initial data close to local minimizers of the Möbius energy the gradient flow exists for all time and converges smoothly to a local minimizer after suitable reparametrizations. To prove this, we show that the heat flow of the Möbius energy possesses a quasilinear structure which allows us to derive new short-time existence results for this evolution equation and a Łojasiewicz-Simon gradient inequality for the Möbius energy.